ECE3300 Lecture 2-1 Electric Fields

Uploaded by cfurse on 24.08.2009

Welcome to ECE3300 at the University of Utah. This is
an introduction to electromagnetics and we are going to
begin with with lecture number one, which is a review
of the electric and magnetic fields, the forces
associated with them and their sources. The electric
field is described by coulomb's law. You've seen
coulomb's law before in physics. What it says is if
you have two like charges, either both positive or both
negative, that they are going to repell. And if you
have two charges of different polarity, a positive and
a negative charge, they are going to tend to attract.
let's call this this charge q1 and lets call this
charge q2. The magnitude of the force associated with
either of these two charges is found by multiplying the
charges q1 x q2 dividing by 4 pie epsilon naught and
then the distant squared between them. This right here
is r12, that's the distance from charge number one to
charge number two. The forces given in newton's, the
charges are given in coulomb's and of course the
distance is given in meters. We all know that the
force is a vector quantity, this force right here is
the force on charge two, caused by charge one and it is
going to be the opposite of the force on charge one,
caused by charge two. So force 1 2 is going to be the
negative of force 2 1. Let's find force 2 1, force 2 1
is going to be the magnitude we have above, q1 divided
by -- sorry q1 x q2 divided by 4pi epsilon naught and
then the distance between them squared. And then we
need to define the direction. The direction right here
is going to be given by a unit vector r from 1 to 2,
and that's unit vector. So r from 1 to 2. Let me draw
that. R is going from one to two. That's the unit
vector that's describing the force on charge two caused
by charge number one. Over here, this would be the
unit vector from 2 to 1. There is a constant that is
important here. It is epsilon naught. It is called
the permittivity or the electrical permittivity. We
can see this is the permittivity of free space because
of the naught or the 0 that is shown here. The
magnitude of permittivity of free space
is 8.854 x 10 to the minus 12 farads per meter.
so this gives you us a complete picture of the force
that is caused by a charge. The electric field is associated
with this force. Let's take a charge right here and a
charge right there, q1, q2 and let's say that we want
to find the electric field right here where q1 is. The
way we do that is we let q1 be one coulomb, sometimes
we call this taking a test chairing of one coulomb, and
putting it at the location we want to find the electric
field. The electric field will be a vector quantity
and it will be q1 x q2 over 4pi epsilon naught, r from
1 to 2 squared and it is going to be in which
direction? Right here. If we want to find the
electric field here we want the force on q1 so e at
location number one is going to be this. It is going
to be r from two to one, and that's going to tell us
the force that happens, that's caused by charge two at
the charge one location. This is the electric field at
that location number one.